One-to-one functions

Question

Suppose the equation f(x)=a has a unique solution x for all numbers a assumed by the function.

 

Is f(x) one-to-one?

Answer 1

Yes, f(x) is one-to-one. One-to-one means that there is only a single output (y) for each input (x), and also there is only a single input (x) that will produce an output (y).  So, for instance, f(x) = x^2, a parabola, is not one-to-one because when y = 4, x can be 2 or -2.  If you were to graph f(x), the graph would pass both the vertical line test and horizontal line test, meaning that the vertical or horizontal line would only pass through the function at most one time.